Question: Rewrite as a simplified fraction. ${0.4\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 46.6666...\\ 10x &= 4.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 42}$ ${x = \dfrac{42}{90}} $ ${x = \dfrac{7}{15}} $